Problem 5. Suppose that A E Rnxd and B E RdXP, and let TA and T's be the linear transforma- tions defined by TA : Red - Rn TA(X) = Ax for all and TB : RP - R TB() = Bx for all T ERP. (a) Prove that AB = 0 if and only if im TB C ker TA. (b) Find two non-zero matrices (of whatever sizes you like) such that AB = 0